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PhD (Business Mathematics and Informatics), North-West University, Potchefstroom Campus, 2016 The thesis consist of four articles presented in seperate chapters, addressing selected subtle issues arising from the arbitrage pricing theory in the real market, with particular focus on derivative instruments and counterparty credit risk. The subtles include modeling of bid-ask spreads, choosing the appropriate interest rate to approximate the risk-free interest rate and modeling of counterparty credit risk. These subtles remain contentious issues in arbitrage pricing theory, hence the major interest to this work. Chapter 2 presents an article which explores arbitrage pricing in the presence of bid-ask spreads modeled using conic finance theory. Conic finance is a brand new quantitative fi nance theory which models bid-ask prices of cash flows by applying the theory of acceptability to cash flows. The theory of acceptability indices combines elements of arbitrage pricing theory and expected utility theory, which captures the preferences of market participants. In the article, the theory is used to assess the risks of equity derivatives trading strategies. Chapter 3 is an article, which is an extension of the theory introduced in the previous chapter. This article explores the theory of conic finance, with particular focus to options on LIBOR based derivative instruments. In the same article, we also explore the dynamics of the options on LIBOR based derivatives. Using the theory, an approach to estimate bid-ask prices for options on LIBOR based instruments is proposed. In particular, the proposed approach is assessed in the determination of premiums for caps and floors. In Chapter 4, an article on simulation techniques that are useful to this work is presented. At the core of the article is comparison of various Monte Carlo methods. In this work the comparison is done in a prediction of stock price movement setup. However, the fi ndings of this work have great bearing on the suitable simulation techniques to be used in subsequent work. Chapter 5 is an article on modeling credit exposures and pricing counterparty credit for OTC interest rate derivatives - caps, floors and swaptions, using the LIBOR Market Model (LMM). In the presence of counterparty credit risk, trades are no longer riskless as impact of counterparty credit risk on arbitrage pricing and hedging strategies can be signifi cant. In the article, the Basel III standardized approach for OTC interest rate derivatives is analyzed with the objective of understanding how the CVA levels evolve under this approach. The reasons for focusing on the standardized approach being that it is widely used in fi nancial institutions and the data required for the standardized approach is easily available. CVA stress tests towards netting agreements, ratings and maturities were implemented using a test portfolio consisting of OTC interest rate derivatives transactions with different counterparties. Doctoral |
